Exact Potts/Tutte polynomials for polygon chain graphs

Coherent and Exact Polygon-to-Polygon Visibility

Visibility computation is a classical problem in computer graphics. A wide variety of algorithms provides solutions with a different accuracy. However, the four dimensional nature of the 3D visibility has prevented for a long time from leading to exact from-polygon visibility algorithms. Recently, the two first tractable solutions were presented by Nirenstein, then Bittner. Their works give the...

Tutte Polynomials of Flower Graphs

Convex Polygon Intersection Graphs

Geometric intersection graphs are graphs determined by the intersections of certain geometric objects. We study the complexity of visualizing an arrangement of objects that induces a given intersection graph. We give a general framework for describing classes of geometric intersection graphs, using arbitrary finite base sets of rationally given convex polygons and rationally-constrained affine ...

Exact Solution of Two Planar Polygon Models

Using a simple transfer matrix approach we have derived long series expansions for the perimeter generating functions of both three-choice polygons and punctured staircase polygons. In both cases we find that all the known terms in the generating function can be reproduced from a linear Fuchsian differential equation of order 8. We report on an analysis of the properties of the differential equ...

321-Polygon-Avoiding Permutations and Chebyshev Polynomials

A 321-k-gon-avoiding permutation π avoids 321 and the following four patterns: k(k + 2)(k + 3) · · · (2k − 1)1(2k)23 · · · (k − 1)(k + 1), k(k + 2)(k + 3) · · · (2k − 1)(2k)12 · · · (k − 1)(k + 1), (k + 1)(k + 2)(k + 3) · · · (2k − 1)1(2k)23 · · · k, (k + 1)(k + 2)(k + 3) · · · (2k − 1)(2k)123 · · · k. The 321-4-gon-avoiding permutations were introduced and studied by Billey and Warrington [BW]...